Many communication networks, such as the Internet, rely on packet switching technologies (e.g., X.25, frame relay, asynchronous transfer mode, etc.) to transport variable or uniform blocks (usually termed packets or cells) of data between nodes. The term packet will be used herein to collectively refer to any such block of information. Such networks generally perform two major functions: routing and congestion control. The object of routing is to deliver, correctly and sometimes in sequence, the packets from a source to a destination. The object of congestion control is to maintain the number of packets within the network (or a region or sub-network thereof) below a level at which queuing delays become excessive. Due to finite resources, packets may be dropped rather than queued.
In essence, a packet switched network is a network of queues communicatively coupled together by communication links (which may be made up of various physical media). At each network node (e.g., a switch or router), there exist one or more queues of packets for each outgoing link. If the rate at which packets arrive and queue up exceeds the rate at which packets are transmitted, queue size grows without bound and the delay experienced by a packet tends towards infinity.
In an ideal case, network throughput, and hence network use, should increase to an offered load up to the physical capacity of the network and remain at capacity if the load is further increased. This ideal case, however, requires that all nodes somehow know the timing and rate of packets that will be presented to the network with no overload and no delay in acquiring this information; a situation which is not possible. If no congestion control is exercised, as the load increases, use increases for a while. Then, as the queue lengths at various nodes begin to grow, throughput actually drops. This is due to the fact that the queues are constrained to a finite length by the physical size of the memories in which they exist. When a node's memory (i.e., its queues) is full, it must drop (i.e., discard) additional incoming packets. Thus, the source is forced to retransmit these packets in addition to any new packets it might have. This only serves to worsen the situation. As more and more packets are retransmitted, the load on the network grows and more and more nodes become saturated. Eventually, even a successfully delivered packet may be retransmitted because it takes so long to get to its destination (whereupon it may be acknowledged by the destination node) that the source actually assumes that the packet was lost and tries to retransmit it. Under such circumstances, the effective capacity of the network can be virtually zero.
Contrary to what one might believe, the solution to this problem is not simply to allow the queue lengths to grow indefinitely. Indeed, it has been shown that even where queue lengths are allowed to be infinite, congestion can occur. See, e.g., John Nagle, “On Packet Switches with Infinite Storage”, Network Working Group, Internet Engineering Task Force, RFC 970 (1985). One reason that this is true is that packets are often coded with an upper bound on their life, thus causing expired packets to be dropped and retransmitted, adding to the already overwhelming volume of traffic within the network.
It is clear that catastrophic network failures due to congestion should (indeed, must) be avoided and preventing such failures is the task of congestion control processes within packet switched networks. To date, however, the object of such congestion control processes has been to limit queue lengths at the various network nodes so as to avoid throughput collapse. Such non-TCP techniques require the transmission of some control information between the nodes and this overhead itself tends to limit the available network bandwidth for data traffic. Nevertheless, a good congestion control process maintains a throughput that differs from a theoretical ideal by an amount roughly equal to its control overhead.
Even these “good” congestion control processes, however, are not good enough. Studies of traffic flow across the Internet show that bandwidth of the various communication links is underutilized even in the presence of congestion. That is, even though excess capacity exists on the communication links that couple various nodes of the Internet to one another, packets are still being dropped within the network. One reason that conventional congestion control processes have failed in this fashion is that such processes do not take into account the true nature of network traffic.
Existing congestion control approaches have generally viewed network traffic (e.g., the generation of new packets to be injected into a network) as essentially random processes. However, recent work in the area of traffic modeling has shown that network traffic is in fact chaotic in nature. None of the currently proposed congestion control methodologies capture or exploit this characteristic.
Other studies from the academic community have shown that the time series of network traffic throughput is not Poisson, but fractal. Namely, the “bursty” behavior seen in a time series at a given time scale is also seen at all other time scales. This “self-similarity” is one of the signatures that characterize a fractal time series. However, as explained in the above-referenced co-pending application, the present applicants have discovered that this “self-similar” signature is not present for heavily congested network traffic. Instead, the present applicants have verified that the traffic generated without any TCP protocol exhibits a fractal time series if the files transmitted are drawn randomly from a Pareto distribution of file sizes. The Fourier power spectrum in this case is a power law that on a log—log scale is linear, as shown in FIG. 1. This power law behavior is another signature of a fractal time series. The present applicants have also discovered that traffic flow with TCP protocol is also fractal, but only if the network topology is under-supplied with traffic. In this situation, the only significant portion of the TCP protocol responsible for the traffic dynamics is the receiver's window size. See FIG. 2. However, when the network topology is congested with traffic, the packet losses coupled with the non-linearity of the TCP congestion avoidance algorithm results in a time series that loses its fractality and multi-fractality. The corresponding Fourier power spectrum shows no power law behavior and is shown in FIG. 3. Even though the time series is not fractal, it is still chaotic.
The term “chaos” is used to describe the apparently random behavior exhibited by many deterministic nonlinear dynamical systems. Such systems manifest a rather remarkable phenomenon in that their deterministic property implies that all future states are determined from the present state. Thus, on one hand there is complete future knowledge of the system, while on the other there is seemingly random motion.
Chaos then is the long-term aperiodic behavior of a deterministic, nonlinear, dynamical system that exhibits sensitivity to initial conditions. Aperiodicity is the property that orbits never repeat themselves exactly; however they may get arbitrarily close to doing so, as observed in periodic windows. The other, perhaps more important, property is the sensitivity of the system to tiny perturbations. Consider two given points in phase space that are distinct but lie arbitrarily close to each other, then one might assume that their orbits will remain close forever. In fact, just the opposite is observed; the orbits separate exponentially in a bounded region of state space.
As indicated above, current congestion control processes simply do not take the chaotic network traffic characteristics into account and, therefore, cannot be expected to be optimum solutions to the congestion problem. To understand why network traffic is chaotic in nature, consider the Internet infrastructure and a series of packet transmissions between a source and a receiver within the Internet.
The Internet infrastructure is complex, with many interconnections between routers. For a given router, there are both incoming connections from various sources and outgoing connections to various receivers. For the most part, the transmissions are controlled using the well-known transmission control protocol (TCP). Very early in the development of the modern Internet, it was discovered that some control over the manner in which packets were injected into the network by the source was needed.
Originally, TCP allowed a source to inject multiple packets into a network, up to a limit corresponding to a window or buffer size advertised by the receiver. Although such a scheme may work where the source and the receiver are connected to the same local area network, it was soon found that where routers having finite buffer sizes are disposed between the source and the receiver, problems arise as these routers soon run out of space to hold the incoming packets. To combat this problem Jacobson and Karels developed a “slow start” procedure wherein the source limits the rate at which it injects new packets into the network according to the rate at which acknowledgements of successful receptions are returned by the receiver. Van Jacobson and Michael J. Karels, “Congestion Avoidance and Control”, Proceedings of SIGCOMM '88 (Stanford, Calif., August 1988), ACM.
Under the slow start procedure, a so-called congestion window is added to the source's TCP implementation. When a connection is established with a resource on another network, this congestion window is initialized to one segment (e.g., the segment or packet size advertised by the resource or a default packet size). Each time an acknowledgement is received, the congestion window is incremented and the source is allowed to inject a number of packets up to the minimum of the current congestion window size or the receiver's advertised window. Over time, the source's congestion window will grow exponentially until at some point the capacity of the intervening network is reached and some intermediate router begins dropping packets. This is an indication to the source that its congestion window has gotten too large. See, e.g., W. Richard Stevens, TCP/IP Illustrated, Vol. 1: The Protocols (1994) and Gary W. Wright and W. Richard Stevens, TCP/IP Illustrated, Vol. 2: The Implementation (1995).
At this point, and where the slow start process is run in concert with a conventional congestion avoidance procedure, the source resets its congestion window to one, and the process repeats up to the point at which the congestion window becomes half the size at which packet loss occurred previously. After this point, the congestion avoidance process takes over and begins incrementing the congestion window in a linear fashion (rather than in an exponential fashion as under the slow start process) in response to receiver acknowledgements.
This sudden change from an exponentially growing number of packets being injected to a linearly growing number of packets being injected presents a discontinuity. Such discontinuities are observed at the intervening router for each of the connections it is servicing. Moreover, the discontinuities appear at random as there is no synchronization between the different sources injecting packets into the network. It is the interaction between the discontinuities that result from the operation of the TCP and the randomness at which they are manifest at the routers within the network that gives rise to the chaotic nature of network (e.g., Internet) traffic.
In such a system it would seem that there is little or no ability to estimate congestion conditions, especially congestion conditions downstream of a point of interest. Nevertheless, in order to control congestion, the ability to accurately make such estimates is critical. The present invention addresses these needs.